Cone structure of L 2-Wasserstein spaces

研究成果: Article

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The aim of this paper is to obtain a better understanding of the geometric structure of quadratic Wasserstein spaces over separable Hilbert spaces. For this sake, we focus on their cone and product structures, and prove that the quadratic Wasserstein space over any separable Hilbert space has a cone structure and splits the underlying space isometrically but no more than that. These are shown in more general settings, and one of our main results is that the quadratic Wasserstein space over a Polish space has a cone structure if and only if so does the underlying space.

元の言語English
ページ(範囲)237-253
ページ数17
ジャーナルJournal of Topology and Analysis
4
発行部数2
DOI
出版物ステータスPublished - 2012 6
外部発表Yes

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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